Remark on the irrationality of the Brun's constant
classification
🧮 math.NT
math.GM
keywords
constantbruncalculatedclosecontinueddenominatorsn-thvalues
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We have calculated numerically geometrical means of the denominators of the continued fraction approximations to the Brun constant B2. We get values close to the Khinchin constant. Next we calculated the n-th square roots of the denominators of the n-th convergents of these continued fractions obtaining values close to the Khinchin-Levy constant. These two results suggests that B2 is irrational, supporting the common believe that there is an infinity of twins.
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